Circle Geometry: Circles in A Equilateral Triangle
Ten equal circular discs can just be placed tightly within a frame in the form of a equilateral triangle. Nine of the them touch the frame; the tenth, in the center, touches six of the other discs. If the internal sides of the frame are each of length measured R, express the radius of each circular disc in terms of R, and show that the outside perimeter of the figure which remains when the frame is removed is:
11/12 (3-sqrt3) (pi) R
Attempted it to no avail. Tried obtaining expression for r (radius of circle) using simultaneous equations. Discovered r = R/2, which is obviously wrong. Please show me how to do this question. Thanks very much.